We characterize when a Hankel operator and a Toeplitz operator have a compact commutator. Let dσ(w) be the normalized Lebesgue measure on the unit circle ∂D. The Hardy space H is the subspace of L(∂D, dσ), denoted by L, which is spanned by the space of analytic polynomials. So there is an orthogonal projection P from L onto the Hardy space H, the so-called Hardy projection. Let f be in L∞. The ...

Let ii be a bounded symmetric domain in C with normalized 2 volume measure dV . Let P be the orthogonal projection from L (il, dV) 2 2 onto the Bergman space La(Q) of holomorphic functions in L (ii, dV). Let P be the orthogonal projection from L (ii, dV) onto the closed subspace of antiholomorphic functions in L (ii, dV). The "little" Hankel operator h, with symbol / is the operator from La(Ci)...

The problem of the minimization of least squares functionals with l penalties is considered in an infinite dimensional Hilbert space setting. While there are several algorithms available in the finite dimensional setting there are only a few of them which come with a proper convergence analysis in the infinite dimensional setting. In this work we provide an algorithm from a class which have not...

We provide an error estimate for the local mean projection approximation in L p([0, τ∗]) for p ∈ [1,+∞[, in terms of the regularity of the underlying grid, and we apply it to the corresponding projection approximation of weakly singular Fredholm integral equations of the second kind. © 2004 Elsevier Ltd. All rights reserved.

The honeybee olfactory system is a well-established model for understanding functional mechanisms of learning and memory. Olfactory stimuli are first processed in the antennal lobe, and then transferred to the mushroom body and lateral horn through dual pathways termed medial and lateral antennal lobe tracts (m-ALT and l-ALT). Recent studies reported that honeybees can perform elemental learnin...

Abstract We review the introduction of several types projection filters. Projection structures coming from information geometry are used to obtain a finite dimensional filter in form stochastic differential equation (SDE), starting exact infinite-dimensional partial (SPDE) for optimal filter. start with Stratonovich filters based on Hellinger distance as introduced and developed Brigo et al. (I...

We show results about the existence and the nonexistence of a projection from the space L(L(λ), X) of all linear and bounded operators from L(λ) into X onto the subspace R(L(λ), X) of all representable operators.

We prove the stability of a weighted L 2 projection operator onto piecewise linear finite elements spaces in Sobolev norm. Namely, we consider orthogonal projections π N,ω from (